What is 5/49 plus 6/21? (Answer: 19/49)

Exact Answer

==================================================
Problem: What is 5/49 plus 6/21?
Formula / Expression: 5/49 + 6/21
Final Answer: 19/49
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 5/49 by 3, and multiply the numerator and denominator of 6/21 by 7 so both fractions share the common base 147.
Working: 5 × 3/49 × 3 = 15/147 and 6 × 7/21 × 7 = 42/147

Step 3: Add the Numerators
Now add the numerators (15 + 42 = 57) and keep the common denominator 147 unchanged.
Working: 15 + 42/147 = 57/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/147 ÷ 3 = 19/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 49 produces a repeating decimal (approximately 0.387755, or 38.7755%).
Working: 19 ÷ 49 = 0.387755 (38.7755%)

Key Values:
- Simplified Fraction: 19/49
- Mixed Number Form: 19/49
- Decimal Value: 0.387755
- Percentage: 38.7755%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-49-plus-6-21/
==================================================

5/49 + 6/21 = 19/49

Simplified Fraction

19/49

Mixed Number

Proper (19/49)

Decimal Value

0.387755

Percentage

38.7755%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 5/49 + 6/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 5/49 by 3, and multiply the numerator and denominator of 6/21 by 7 so both fractions share the common base 147.

5 × 3/49 × 3 = 15/147 and 6 × 7/21 × 7 = 42/147

Step 3

Add the Numerators

Now add the numerators (15 + 42 = 57) and keep the common denominator 147 unchanged.

15 + 42/147 = 57/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 147, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/147 ÷ 3 = 19/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 49 produces a repeating decimal (approximately 0.387755, or 38.7755%).

19 ÷ 49 = 0.387755 (38.7755%)

Visual Representation

The diagram below illustrates 5/49 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/49`
Mixed Number Form	`19/49`
Decimal Form	`0.387755`
Percentage	`38.7755%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/49 plus 6/21 as a fraction?

5/49 + 6/21 in simplest fraction form is 19/49.

What is 5/49 plus 6/21 as a decimal?

5/49 + 6/21 converted to a decimal is 0.387755.

What is 5/49 plus 6/21 as a percentage?

5/49 + 6/21 expressed as a percentage is 38.7755%.

Does 5/49 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.387755...) because the denominator contains prime factors other than 2 and 5.